Finite Group Databasebeta

← #11900910

Subgroups — #11900910

Order 1152.

2579 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic, complemented
2C3×C4×#235C211yesmaximal, characteristic, complemented
3C2×C3×C42×D3C211yesmaximal, characteristic, complemented
4#10595049C211yesmaximal, characteristic, complemented
5#10595029C211yesmaximal, characteristic, complemented
6#10595023C211yesmaximal, characteristic, complemented
7#10595022C211yesmaximal, characteristic, complemented
8#10595002C214yesmaximal, complemented
9#10594839C214yesmaximal, complemented
10#10593974C212yesmaximal, complemented
11#10593973C214yesmaximal, complemented
12#10593968C212yesmaximal, complemented
13C4×#3798C214yesmaximal, complemented
14#10593873C212yesmaximal, complemented
15#10593870C212yesmaximal, complemented
16#85836—31nomaximal
17#85680—31nomaximal
18C2×#3828C2211yescharacteristic
19C2×C3×#235C2211yescharacteristic
20C22×C3×C4×D3C2212yes—
21C22×C3×C4×D3C2211yescharacteristic
22C2×#3798C2214yes—
23C2×C32×C42C2211yescharacteristic
24C4×#638C2214yes—
25#64135C2211yescharacteristic
26C4×C4⋊(C3⋊D3)C2212yescomplemented
27#64081C2212yescomplemented
28C42×C3⋊D3C2212yescomplemented
29C4×#634C2212yescomplemented
30C3×C4×#67C2214yes—
31C3×#926C2211yescharacteristic
32C2×C3×C4×Dic3C2212yes—
33C2×C3×C4×Dic3C2211yescharacteristic
34C3×C4×D12C2212yescomplemented
35C3×#872C2212yescomplemented
36C3×C42×D3C2212yes—
37C3×C42×D3C2212yes—
38C3×C42×D3C2212yes—
39C3×C42×D3C2212yes—
40C3×C42×D3C2212yescomplemented
41C3×C4×Dic6C2212yescomplemented
42#63978C2214yes—
43#63977C2212yes—
44#63976C2212yes—
45#63966C2212yes—
46#63964C2214yes—
47#63961C2212yes—
48#63918C2212yescomplemented
49C4×#627C2214yescomplemented
50C4×#627C2214yescomplemented
51#63911C2211yescharacteristic, complemented
52#63909C2212yes—
53#63908C2212yes—
54#63906C2214yes—
55#63905C2214yes—
56C4×#626C2214yes—
57C4×#626C2214yes—
58C4×#626C2214yescomplemented
59C4×#626C2214yescomplemented
60C4×#625C2214yes—
61C4×#625C2214yes—
62#63874C2214yescomplemented
63#63869C2212yescomplemented
64#63868C2214yescomplemented
65#63867C2214yescomplemented
66#63866C2211yescharacteristic, complemented
67#63864C2211yescharacteristic, complemented
68#63860C2211yescharacteristic, complemented
69#63859C2214yescomplemented
70#63857C2212yes—
71#63856C2212yes—
72#63855C2214yes—
73#63855C2214yescomplemented
74#63852C2214yescomplemented
75#63851C2214yes—
76#63850C2214yes—
77C3×C4×#41—31no—
78C22×C3×C42—31no—
79#5832—31no—
80#5828—31no—
81#5791—31no—
82#5791—34no—
83#5791—31no—
84#5580—32no—
85#5578—32no—
86#5557—32no—
87#5548—32no—
88#5547—34no—
89#5538—34no—
90#5528—34no—
91#5524—31no—
92#5517—31no—
93#5479—34no—
94#5479—32no—
95#5479—34no—
96#5479—32no—
97#5477—31no—
98#5477—32no—
99C4×#235—31no—
100C4×#235—31no—
101C4×#235—34no—
102C4×#235—34no—
103C4×#235—61no—
104C4×#235D311yescharacteristic, complemented
105C2×C42×D3D311yescharacteristic, complemented
106#5470—31no—
107#5470—32no—
108C23×C3×D3C2311yescharacteristic
109C22×C32×C4C2312yes—
110C22×C32×C4C2311yescharacteristic
111C2×#638C2312yes—
112#3828—24no—
113C2×C4⋊(C3⋊D3)C2311yescharacteristic
114C2×C4×C3⋊D3C2314yes—
115C2×C4×C3⋊D3C2312yes—
116C2×#634C2311yescharacteristic
117C2×C3×#67C2312yes—
118C22×C3×Dic3C2311yescharacteristic
119C22×C3×Dic3C2312yes—
120C3×#235—24no—
121C2×C3×D12C2311yescharacteristic
122C2×C3×C4×D3—24no—
123C2×C3×C4×D3—28no—
124C2×C3×C4×D3C2314yes—
125C2×C3×C4×D3C2312yes—
126C2×C3×C4×D3C2312yes—
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2312yes—
129C2×C3×C4×D3C2312yes—
130C2×C3×C4×D3C2312yes—
131C2×C3×C4×D3C2312yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×#627C2314yes—
134C2×#626C2314yes—
135C2×#626C2314yes—
136C2×#625C2314yes—
137#3798—216no—
138C32×C42C2312yes—
139C32×C42C2311yescharacteristic
140C32×C42C2311yescharacteristic
141#3757C2312yes—
142#3752C2314yes—
143C4⋊(C3⋊Dic3)C2312yes—
144#3750C2314yes—
145C4×C3⋊Dic3C2314yes—
146C4×C3⋊Dic3C2312yes—
147C3×#217C2312yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×C4⋊Dic3C2312yes—
150C3×Dic3⋊C4C2314yes—
151C3×C4×Dic3C2312yes—
152C3×C4×Dic3C2312yes—
153C3×C4×Dic3C2312yes—
154C3×C4×Dic3C2311yescharacteristic
155C3×C4×Dic3C2311yescharacteristic
156C3×C4×Dic3C2312yes—
157C3×C4×Dic3C2312yes—
158C3×C4×Dic3C2312yes—
159C3×C4×Dic3C2314yes—
160#3724C2314yes—
161#3724C2314yes—
162Dic3⋊Dic3C2314yes—
163Dic3⋊Dic3C2314yes—
164Dic3⋊Dic3C2314yes—
165Dic3⋊Dic3C2314yes—
166#3722C2314yes—
167#3722C2314yes—
168(C2×D3)⋊Dic3C2314yes—
169(C2×D3)⋊Dic3C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2314yes—
172#3444—91noSylow
173C2×C3×#41—31no—
174C23×C3×C4—32no—
175C23×C3×C4—31no—
176C2×#235—31no—
177C2×#235—31no—
178C2×#235—34no—
179C2×#235—34no—
180C2×#235—61no—
181C2×#235C2×D311yescharacteristic
182C22×C4×D3C2×D311yescharacteristic
183C22×C4×D3C2×D312yes—
184C3×C4×Q8—32no—
185C3×C4×D4—34no—
186C3×C4×D4—32no—
187C3×#117—31no—
188C3×#117—32no—
189C2×C3×C42—21no—
190C2×C3×C42—31no—
191C2×C3×C42—32no—
192C2×C3×C42—32no—
193C2×C3×C42—32no—
194C2×C3×C42—32no—
195C2×C3×C42—32no—
196C2×C3×C42—32no—
197C2×C3×C42C2×D311yescharacteristic
198C2×C3×C42C2×D311yescharacteristic
199#953—32no—
200#953—32no—
201#947—31no—
202#946—32no—
203#944—31no—
204#940—31no—
205#939—34no—
206#938—32no—
207#937—32no—
208#936—31no—
209#935—32no—
210#930—34no—
211#930—32no—
212#930—34no—
213#930—32no—
214#929—32no—
215#929—32no—
216#929—34no—
217#929—34no—
218C4×#67—34no—
219C4×#67—34no—
220C4×#67—34no—
221C4×#67—34no—
222C4×#67—34no—
223C4×#67—34no—
224C4×#67—34no—
225C4×#67—34no—
226C4×#67—34no—
227C4×#67—34no—
228C4×#67—64no—
229C4×#67C2×D314yes—
230#926—31no—
231#926—31no—
232#926—34no—
233#926—34no—
234#926—61no—
235#926C2×D311yescharacteristic
236#924—32no—
237#924—34no—
238#924—32no—
239#924—34no—
240C2×C4×Dic3C2×D311yescharacteristic
241C2×C4×Dic3C2×D312yes—
242#898—34no—
243#897—32no—
244#896—34no—
245#895—32no—
246#894—34no—
247#890—32no—
248#889—34no—
249#888—32no—
250#886—32no—
251#885—34no—
252#884—34no—
253#883—34no—
254#882—32no—
255#879—34no—
256#878—34no—
257#876—34no—
258#876—34no—
259#875—31no—
260#875—31no—
261#875—34no—
262#874—31no—
263C4×D12—34no—
264C4×D12—34no—
265C4×D12—34no—
266C4×D12—34no—
267C4×D12—32no—
268C4×D12—32no—
269C4×D12—62no—
270C4×D12C2×D312yescomplemented
271#872—34no—
272#872—34no—
273#872—32no—
274#872—32no—
275#872—34no—
276#872—34no—
277#872—62no—
278#872C2×D312yescomplemented
279C42×D3—32no—
280C42×D3—32no—
281C42×D3—62no—
282C42×D3C2×D312yes—
283C42×D3C2×D312yes—
284C42×D3C2×D312yes—
285C42×D3C2×D312yes—
286C42×D3C2×D312yescomplemented
287#870—32no—
288#870—34no—
289#869—31no—
290#869—32no—
291C4×Dic6—32no—
292C4×Dic6—32no—
293C4×Dic6—34no—
294C4×Dic6—34no—
295C4×Dic6—34no—
296C4×Dic6—34no—
297C4×Dic6—62no—
298C4×Dic6C2×D312yescomplemented
299C23×C32C2411yescharacteristic
300C22×C3⋊D3C2412yes—
301C22×C3×D3—22no—
302C22×C3×D3—24no—
303C22×C3×D3C2412yes—
304C22×C3×D3C2412yes—
305C2×C32×C4—24no—
306C2×C32×C4#4114yescomplemented
307C2×C32×C4C2412yes—
308C2×C32×C4C2411yescharacteristic
309C2×C32×C4C2412yes—
310C2×C32×C4C2411yescharacteristic
311#638—24no—
312C2×C3⋊Dic3C2412yes—
313C2×C3⋊Dic3C2414yes—
314C4⋊(C3⋊D3)—22no—
315C4×C3⋊D3—24no—
316C4×C3⋊D3—28no—
317#634—22no—
318C3×#67—24no—
319C2×C3×Dic3—22no—
320C2×C3×Dic3—24no—
321C2×C3×Dic3C2412yes—
322C2×C3×Dic3C2412yes—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2414yes—
325C2×C3×Dic3C2412yes—
326C3×D12—22no—
327C3×C4×D3—24no—
328C3×C4×D3—28no—
329C3×C4×D3—24no—
330C3×C4×D3—24no—
331C3×C4×D3—24no—
332C3×C4×D3—24no—
333C3×C4×D3—24no—
334C3×C4×D3#4118yescomplemented
335C3×Dic6—22no—
336#627—28no—
337#626—28no—
338#626—28no—
339#625—28no—
340#533—91no—
341#533—92no—
342#532—92no—
343#532—91no—
344#529—94no—
345#529—94no—
346#529—92no—
347#529—92no—
348#525—91no—
349#525—94no—
350#525—91no—
351C4×#41—31no—
352C4×#41—94no—
353C4×#41—91no—
354C22×C42—31no—
355C24×C3—31no—
356C23×D3C22×D311yescharacteristic
357C3×#41—64no—
358C2×C3×Q8—31no—
359C2×C3×D4—32no—
360C2×C3×D4—31no—
361C22×C3×C4—21no—
362C22×C3×C4—22no—
363C22×C3×C4—32no—
364C22×C3×C4—32no—
365C22×C3×C4—31no—
366C22×C3×C4—32no—
367C22×C3×C4—32no—
368C22×C3×C4—34no—
369C22×C3×C4—32no—
370C22×C3×C4—32no—
371C22×C3×C4—32no—
372C22×C3×C4—32no—
373C22×C3×C4—68no—
374C22×C3×C4—64no—
375C22×C3×C4C22×D312yes—
376C22×C3×C4C22×D312yes—
377C22×C3×C4C22×D311yescharacteristic
378C22×C3×C4C22×D311yescharacteristic
379C2×#67—32no—
380C2×#67—32no—
381C2×#67—34no—
382C2×#67—34no—
383C2×#67—34no—
384C2×#67—34no—
385C2×#67—62no—
386C2×#67C22×D312yes—
387C22×Dic3C22×D312yes—
388C22×Dic3C22×D311yescharacteristic
389#235—24no—
390#235—616no—
391#235—68no—
392#235—64no—
393#235—64no—
394#235—616no—
395C2×D12—34no—
396C2×D12—34no—
397C2×D12—31no—
398C2×D12—31no—
399C2×D12—61no—
400C2×D12C22×D311yescharacteristic
401C2×C4×D3—24no—
402C2×C4×D3—28no—
403C2×C4×D3—32no—
404C2×C4×D3—32no—
405C2×C4×D3—34no—
406C2×C4×D3—34no—
407C2×C4×D3—62no—
408C2×C4×D3—64no—
409C2×C4×D3C22×D312yes—
410C2×C4×D3C22×D312yes—
411C2×C4×D3C22×D312yes—
412C2×C4×D3C22×D312yes—
413C2×C4×D3C22×D312yes—
414C2×C4×D3C22×D314yes—
415C2×C4×D3C22×D312yes—
416C2×C4×D3C22×D312yes—
417C2×Dic6—31no—
418C2×Dic6—31no—
419C2×Dic6—34no—
420C2×Dic6—34no—
421C2×Dic6—61no—
422C2×Dic6C22×D311yescharacteristic
423C3×C4⋊C4—32no—
424C3×C4⋊C4—34no—
425C3×C22⋊C4—32no—
426C3×C22⋊C4—34no—
427C3×C42—22no—
428C3×C42—21no—
429C3×C42—21no—
430C3×C42—32no—
431C3×C42—32no—
432C3×C42—32no—
433C3×C42—34no—
434C3×C42—31no—
435C3×C42—32no—
436C3×C42—31no—
437C3×C42—32no—
438C3×C42—32no—
439C3×C42C22×D312yes—
440C3×C42C22×D312yes—
441C3×C42C22×D311yescharacteristic
442C3×C42C22×D311yescharacteristic
443C3×C42C22×D311yescharacteristic
444C3×C42C22×D311yescharacteristic
445#217—32no—
446#217—32no—
447#217—34no—
448#217—34no—
449#217—34no—
450#217—34no—
451#217—62no—
452#217C22×D312yes—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4—34no—
457(C2×D3)⋊C4—34no—
458(C2×D3)⋊C4—34no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—34no—
461(C2×D3)⋊C4—34no—
462(C2×D3)⋊C4—34no—
463(C2×D3)⋊C4—64no—
464(C2×D3)⋊C4C22×D314yes—
465C4⋊Dic3—32no—
466C4⋊Dic3—32no—
467C4⋊Dic3—34no—
468C4⋊Dic3—34no—
469C4⋊Dic3—34no—
470C4⋊Dic3—34no—
471C4⋊Dic3—62no—
472C4⋊Dic3C22×D312yes—
473Dic3⋊C4—34no—
474Dic3⋊C4—34no—
475Dic3⋊C4—34no—
476Dic3⋊C4—34no—
477Dic3⋊C4—34no—
478Dic3⋊C4—34no—
479Dic3⋊C4—34no—
480Dic3⋊C4—34no—
481Dic3⋊C4—34no—
482Dic3⋊C4—34no—
483Dic3⋊C4—64no—
484Dic3⋊C4C22×D314yes—
485C4×Dic3—34no—
486C4×Dic3—32no—
487C4×Dic3—32no—
488C4×Dic3—34no—
489C4×Dic3—64no—
490C4×Dic3—62no—
491C4×Dic3C22×D312yes—
492C4×Dic3C22×D312yes—
493C4×Dic3C22×D312yes—
494C4×Dic3C22×D314yes—
495C4×Dic3C22×D312yes—
496C4×Dic3C22×D312yes—
497C4×Dic3C22×D312yes—
498C4×Dic3C22×D311yescharacteristic
499C4×Dic3C22×D311yescharacteristic
500C22×C32—22no—
501C22×C32C2×#4112yes—
502C22×C32C2511yescharacteristic
503C2×C3⋊D3—22no—
504C2×C3⋊D3—24no—
505C2×C3×D3—28no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—24no—
509C2×C3×D3—22no—
510C2×C3×D3C2×#4114yes—
511C32×C4—22no—
512C32×C4C2×#4112yes—
513C32×C4C2×#4112yes—
514C32×C4C2×#4114yes—
515C3⋊Dic3—22no—
516C3⋊Dic3—24no—
517C3×Dic3—24no—
518C3×Dic3—22no—
519C3×Dic3—22no—
520C3×Dic3—22no—
521C3×Dic3C2×#4114yes—
522C2×#41—31no—
523C2×#41—94no—
524C2×#41—91no—
525C23×C4—32no—
526C23×C4—31no—
527C4⋊Q8—92no—
528C4⋊Q8—91no—
529#127—91no—
530#126—94no—
531#126—94no—
532#125—94no—
533#125—92no—
534#124—94no—
535#124—91no—
536#124—91no—
537#123—94no—
538#123—92no—
539#123—94no—
540#123—92no—
541C22⋊Q8—94no—
542C22⋊Q8—94no—
543C22⋊Q8—92no—
544C22⋊Q8—92no—
545#121—94no—
546#121—92no—
547#121—92no—
548#121—94no—
549#120—92no—
550#120—92no—
551C4×Q8—32no—
552C4×Q8—94no—
553C4×Q8—94no—
554C4×Q8—92no—
555C4×D4—34no—
556C4×D4—32no—
557C4×D4—94no—
558C4×D4—94no—
559C4×D4—94no—
560C4×D4—94no—
561C4×D4—94no—
562C4×D4—94no—
563C4×D4—94no—
564C4×D4—92no—
565#117—31no—
566#117—32no—
567#117—94no—
568#117—94no—
569#117—94no—
570#117—91no—
571#117—92no—
572C2×C42—32no—
573C2×C42—31no—
574C2×C42—32no—
575C2×C42—32no—
576C2×C42—32no—
577C2×C42—32no—
578C2×C42—32no—
579C2×C42—92no—
580C2×C42D3211yescharacteristic
581C23×C3—21no—
582C23×C3—32no—
583C23×C3—32no—
584C23×C3—64no—
585C23×C3—62no—
586C23×C3C23×D311yescharacteristic
587C23×C3C23×D311yescharacteristic
588C22×D3—22no—
589C22×D3—24no—
590C22×D3—32no—
591C22×D3—32no—
592C22×D3—62no—
593C22×D3C23×D312yes—
594C22×D3C23×D312yes—
595C3×Q8—62no—
596C3×D4—64no—
597C3×D4—62no—
598C2×C3×C4—24no—
599C2×C3×C4—24no—
600C2×C3×C4—21no—
601C2×C3×C4—22no—
602C2×C3×C4—21no—
603C2×C3×C4—22no—
604C2×C3×C4—24no—
605C2×C3×C4—32no—
606C2×C3×C4—38no—
607C2×C3×C4—32no—
608C2×C3×C4—32no—
609C2×C3×C4—32no—
610C2×C3×C4—34no—
611C2×C3×C4—44no—
612C2×C3×C4—64no—
613C2×C3×C4—64no—
614C2×C3×C4—64no—
615C2×C3×C4—62no—
616C2×C3×C4—68no—
617C2×C3×C4—64no—
618C2×C3×C4—64no—
619C2×C3×C4—64no—
620C2×C3×C4—64no—
621C2×C3×C4#23514yescomplemented
622C2×C3×C4#23514yescomplemented
623C2×C3×C4C23×D312yes—
624C2×C3×C4C23×D312yes—
625C2×C3×C4C23×D311yescharacteristic
626C2×C3×C4C23×D311yescharacteristic
627C2×C3×C4C23×D312yes—
628C2×C3×C4C23×D311yescharacteristic
629C2×C3×C4C23×D311yescharacteristic
630C2×C3×C4C23×D312yes—
631#67—24no—
632#67—68no—
633#67—68no—
634#67—68no—
635#67—64no—
636#67—64no—
637#67—68no—
638#67—68no—
639C2×Dic3—22no—
640C2×Dic3—24no—
641C2×Dic3—32no—
642C2×Dic3—34no—
643C2×Dic3—32no—
644C2×Dic3—34no—
645C2×Dic3—62no—
646C2×Dic3—64no—
647C2×Dic3C23×D312yes—
648C2×Dic3C23×D312yes—
649C2×Dic3C23×D314yes—
650C2×Dic3C23×D312yes—
651C2×Dic3C23×D312yes—
652D12—22no—
653D12—64no—
654D12—68no—
655D12—68no—
656D12—62no—
657D12—62no—
658C4×D3—24no—
659C4×D3—24no—
660C4×D3—24no—
661C4×D3—24no—
662C4×D3—24no—
663C4×D3—28no—
664C4×D3—24no—
665C4×D3—68no—
666C4×D3—64no—
667C4×D3—64no—
668C4×D3—68no—
669C4×D3—68no—
670C4×D3—128no—
671C4×D3#23518yescomplemented
672Dic6—22no—
673Dic6—68no—
674Dic6—64no—
675Dic6—62no—
676Dic6—62no—
677Dic6—68no—
678C2×C32—22no—
679C2×C32C22×#4111yescharacteristic
680C2×C32C22×#4112yes—
681C3⋊D3—42no—
682C3×D3—24no—
683C3×D3—42no—
684C24—31no—
685#41—64no—
686#41—1816no—
687#41—184no—
688C2×Q8—31no—
689C2×Q8—94no—
690C2×Q8—91no—
691C2×D4—32no—
692C2×D4—31no—
693C2×D4—94no—
694C2×D4—94no—
695C2×D4—94no—
696C2×D4—92no—
697C2×D4—91no—
698C22×C4—32no—
699C22×C4—32no—
700C22×C4—31no—
701C22×C4—32no—
702C22×C4—32no—
703C22×C4—32no—
704C22×C4—32no—
705C22×C4—32no—
706C22×C4—32no—
707C22×C4—34no—
708C22×C4—68no—
709C22×C4—64no—
710C22×C4—92no—
711C22×C4—94no—
712C22×C4C2×D3212yes—
713C22×C4C2×D3211yescharacteristic
714C4⋊C4—32no—
715C4⋊C4—34no—
716C4⋊C4—94no—
717C4⋊C4—94no—
718C4⋊C4—94no—
719C4⋊C4—94no—
720C4⋊C4—94no—
721C4⋊C4—94no—
722C4⋊C4—92no—
723C4⋊C4—94no—
724C22⋊C4—32no—
725C22⋊C4—34no—
726C22⋊C4—94no—
727C22⋊C4—94no—
728C22⋊C4—94no—
729C22⋊C4—94no—
730C22⋊C4—94no—
731C22⋊C4—94no—
732C22⋊C4—92no—
733C22⋊C4—94no—
734C42—32no—
735C42—32no—
736C42—32no—
737C42—32no—
738C42—31no—
739C42—32no—
740C42—31no—
741C42—32no—
742C42—34no—
743C42—92no—
744C42—94no—
745C42C2×D3211yescharacteristic
746C42C2×D3212yes—
747C42C2×D3211yescharacteristic
748C22×C3—22no—
749C22×C3—22no—
750C22×C3—22no—
751C22×C3—21no—
752C22×C3—34no—
753C22×C3—42no—
754C22×C3—68no—
755C22×C3—62no—
756C22×C3—62no—
757C22×C3—64no—
758C22×C3—62no—
759C22×C3C2×#23512yes—
760C22×C3C2×#23512yes—
761C22×C3C24×D311yescharacteristic
762C22×C3C24×D311yescharacteristic
763C2×D3—28no—
764C2×D3—22no—
765C2×D3—22no—
766C2×D3—22no—
767C2×D3—24no—
768C2×D3—64no—
769C2×D3—62no—
770C2×D3—62no—
771C2×D3—64no—
772C2×D3—64no—
773C2×D3—124no—
774C2×D3C2×#23514yes—
775C3×C4—22no—
776C3×C4—22no—
777C3×C4—22no—
778C3×C4—22no—
779C3×C4—24no—
780C3×C4—34no—
781C3×C4—42no—
782C3×C4—64no—
783C3×C4—62no—
784C3×C4—62no—
785C3×C4—62no—
786C3×C4C2×#23512yes—
787C3×C4C2×#23512yes—
788C3×C4C2×#23512yes—
789C3×C4C2×#23512yes—
790C3×C4C2×#23514yes—
791C3×C4D3×#4114yes—
792Dic3—22no—
793Dic3—22no—
794Dic3—22no—
795Dic3—24no—
796Dic3—64no—
797Dic3—62no—
798Dic3—62no—
799Dic3—64no—
800Dic3—64no—
801Dic3—124no—
802Dic3C2×#23514yes—
803C32#344411yescharacteristic, complemented, Sylow
804C23—32no—
805C23—32no—
806C23—64no—
807C23—62no—
808C23—92no—
809C23C22×D3211yescharacteristic
810Q8—62no—
811Q8—188no—
812Q8—182no—
813D4—64no—
814D4—62no—
815D4—188no—
816D4—188no—
817D4—188no—
818D4—184no—
819D4—182no—
820C2×C4—24no—
821C2×C4—32no—
822C2×C4—38no—
823C2×C4—32no—
824C2×C4—32no—
825C2×C4—34no—
826C2×C4—32no—
827C2×C4—64no—
828C2×C4—64no—
829C2×C4—64no—
830C2×C4—62no—
831C2×C4—64no—
832C2×C4—64no—
833C2×C4—64no—
834C2×C4—64no—
835C2×C4—68no—
836C2×C4—92no—
837C2×C4—94no—
838C2×C4—184no—
839C2×C4—188no—
840C2×C4#379814yescomplemented
841C2×C4C22×D3212yes—
842C2×C4C22×D3211yescharacteristic
843C2×C4C22×D3211yescharacteristic
844C2×C4C22×D3212yes—
845C2×C3—22no—
846C2×C3—22no—
847C2×C3—21no—
848C2×C3—22no—
849C2×C3—42no—
850C2×C3—64no—
851C2×C3—122no—
852C2×C3C22×#23511yescharacteristic
853C2×C3C22×#23511yescharacteristic
854C2×C3C22×#23512yes—
855C2×C3C2×D3×#4112yes—
856D3—24no—
857D3—42no—
858D3—124no—
859D3—122no—
860D3—122no—
861C22—22no—
862C22—34no—
863C22—68no—
864C22—62no—
865C22—62no—
866C22—62no—
867C22—64no—
868C22—182no—
869C22—184no—
870C22C2×#379812yes—
871C22C23×D3211yescharacteristic
872C4—22no—
873C4—34no—
874C4—62no—
875C4—62no—
876C4—62no—
877C4—64no—
878C4—182no—
879C4—184no—
880C4C2×#379812yes—
881C4C2×#379812yes—
882C4D3×#23514yes—
883C3—21no—
884C3#8568011yescharacteristic, complemented
885C3#8583611yescharacteristic, complemented
886C2—22no—
887C2—64no—
888C2—122no—
889C2—362no—
890C2C22×#379811yescharacteristic
891C2C2×D3×#23512yes—
subgroupG/H
centerC42C2×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3444
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C42 ◁ C2×C42

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C4×#3828C2semidirect
2. C3×C4×#235C2semidirect
3. C2×C3×C42×D3C2semidirect
4. #10595049C2semidirect
5. #10595029C2semidirect
6. #10595023C2semidirect
7. #10595022C2semidirect
8. #10595002C2semidirect
9. #10594839C2semidirect
10. #10593974C2semidirect
11. #10593973C2semidirect
12. #10593968C2semidirect
13. C4×#3798C2semidirect
14. #10593873C2semidirect
15. #10593870C2semidirect
26. C4×C4⋊(C3⋊D3)C22semidirect
27. #64081C22semidirect
28. C42×C3⋊D3C22semidirect
29. C4×#634C22semidirect
34. C3×C4×D12C22semidirect
35. C3×#872C22semidirect
40. C3×C42×D3C22semidirect
41. C3×C4×Dic6C22semidirect
48. #63918C22semidirect
49. C4×#627C22semidirect
50. C4×#627C22semidirect
51. #63911C22semidirect
58. C4×#626C22semidirect
59. C4×#626C22semidirect
62. #63874C22semidirect
63. #63869C22semidirect
64. #63868C22semidirect
65. #63867C22semidirect
66. #63866C22semidirect
67. #63864C22semidirect
68. #63860C22semidirect
69. #63859C22semidirect
73. #63855C22semidirect
74. #63852C22semidirect
104. C4×#235D3semidirect
105. C2×C42×D3D3semidirect
270. C4×D12C2×D3semidirect
278. #872C2×D3semidirect
286. C42×D3C2×D3semidirect
298. C4×Dic6C2×D3semidirect
306. C2×C32×C4#41semidirect
334. C3×C4×D3#41semidirect
621. C2×C3×C4#235semidirect
622. C2×C3×C4#235semidirect
671. C4×D3#235semidirect
803. C32#3444semidirect
840. C2×C4#3798semidirect
884. C3#85680semidirect
885. C3#85836semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C4×#38282
C3×C4×#2352
C2×C3×C42×D32
#105950492
#105950292
#105950232
#105950222
#105950022
#105948392
#105939742
#105939732
#105939682
C4×#37982
#105938732
#105938702
#858363
#856803